Electron backscatter diffraction analysis is a well established technique of materials analysis. It is a crystallographic method used to identify materials, phases, grain orientation and texture on the micro-scale, as well as to map strain and characterise defects, and relies on analysis of electron “Kikuchi” patterns obtained using a focused electron beam in a scanning electron microscope, either in a backscattered or a transmission geometry. A typical Kikuchi pattern is shown in FIG. 1.
Various numerical methods have been devised to obtain such information from Kikuchi diffraction patterns of crystals, these all requiring a compromise between computational load and accuracy of measurement. Commonly, analysis methods for Kikuchi patterns rely on the “2D Hough transform” approach, where an area of interest is selected on the Kikuchi pattern and a 2D Hough transform is applied to highlight and locate line structure in the pattern corresponding to the Kikuchi bands, as published by N C Krieger Lassen, “Automated Determination of Crystal Orientations from Electron Backscattering Patterns”, Ph.D Thesis 1994, Technical University of Denmark, DK-2800 Lyngby. Kikuchi bands are revealed as local peaks in the resulting Hough space and their corresponding maxima are found automatically, thus detecting the position and orientation of Kikuchi bands and their corresponding diffraction planes. These detected planes are queried against a database of known phases, and the orientation of the now identified crystal phase is calculated with respect to the overall specimen geometry. Precision and accuracy of this process are limited primarily by the precision of identifying and locating the Kikuchi bands, which in turn is limited by the Hough transform. FIG. 2 shows how pairs of Kikuchi lines are described in the polar parameters (rho, phi) for the Hough transform. The distance L in FIG. 2 indicates the width of the band. The precision in the orientation measurement is, in a first instance, improved by increasing the resolution of the Hough transform and the resulting Hough space, however this results in a much increased computational effort and is undesirable. Further, the Hough transform makes the assumption that the bands are straight segments with constant separation L, whereas Kikuchi bands are hyperbolic, and therefore a systematic error is introduced by the conventional Hough transform, which cannot be overcome through increased Hough space resolution. These problems of precision and accuracy have been addressed by a number of investigators.
A first method, published by C Maurice and R Fortunier, “A 3D Hough transform for indexing EBSD and Kossel patterns”, Journal of Microscopy, vol. 230, 2008, pp. 520-529, consists of extending the Hough transform such that it identifies hyperbolic curves rather than straight lines, where a new hyperbola variable is used in addition to the conventional distance and angle variables. This “Sin theta” variable, which is proportional to the width of the band, L, represents the Bragg reflection condition, However, without knowledge of the crystalline structure, this hyperbola parameter is unknown at the time of the Hough transform and therefore must be varied over a specified range to explore all possible Bragg angles that govern the separation of the two hyperbolic edges for the band. The result of this extended Hough transform is a three-dimensional space (illustrated in FIG. 3), where the third dimension is given by the hyperbola variable, and a given point in this space represents a unique conic section as opposed to just a straight line as with the conventional 2D Hough transform. As with the conventional method, the corresponding local peaks in this three-dimensional space need to be detected to identify the diffraction parameters. Whilst this modified Hough transform removes the systematic error of the conventional Hough transform, it is computationally expensive due to the large three dimensional calculation space, and is therefore slow.
A second method, was reported by J A Small and J R Michael, “Phase identification of individual crystalline particles by electron backscatter diffraction”, Journal of Microscopy, 201(1), 2001, pp. 59-69, and consists of using the band information provided by the 2D Hough method to find the closest match in a database of phases. Using data for the best candidate phase the expected bands are simulated using the correct hyperbolic shape and compared with the measured pattern to provide a visual confirmation that the correct phase has been identified.
In a third method, D J Dingley and S I Wright, “Phase Identification Through Symmetry Determination in EBSD Patterns” book chapter in “Electron Backscatter Diffraction in Materials Science Second Edition”, Springer 2009, ISBN 978-0-387-88135-5, pages 99-103, use additional symmetry measures to find potential candidate phases. Having found a candidate that would generate a pattern with the observed symmetry, they simulate the pattern and vary the lattice parameter in small increments until there is good visual correspondence with some of the bands in the measured pattern.
The second and third methods involve user interaction (such as visual observation) to validate an accurate simulation against the observed pattern and the first method is computationally expensive.
There is a general and long standing need for a practical analysis method with much improved precision and reduced computational load, that does not require manual intervention and this is the object of the present invention.